Low-noise active rc signal processing circuit

ABSTRACT

Disclosed is a low-noise active RC signal processing circuit, which comprises a feedforward section operable responsive to an input signal to provide an output at a predetermined gain, and a feedback section operable responsive to the output of the forward circuit to negatively feed back the output to the input signal of the feedforward section while giving a predetermined transfer characteristic to the output, so as to allow the processing circuit to have a transfer impedance characteristic equal to or less than the predetermined gain over the entire frequency range. The feedforward section is composed of a current-controlled voltage output circuit which includes a common-base transistor for receiving and inverting the input signal, and an emitter-follower transistor for outputting voltage, and has a transfer impedance defining the predetermined gain. The current-controlled voltage output circuit may also be constructed using an operational amplifier. Various filters, such as a bandpass, lowpass or highpass filter, can be achieved by arranging the transfer impedance characteristic. The present invention can provide an active RC signal processing circuit having a low Q-value and an excellent low-noise performance.

TECHNICAL FIELD

[0001] The present invention relates to a low-noise active RC(resistor-capacitor) signal processing circuit, and more particularly toa low-noise active RC signal processing circuit operable to reduce gainover the entire frequency range through negative feedback so as toobtain transfer impedance characteristics suitable for a bandpassfilter, lowpass filter or highpass filter.

BACKGROUND ART

[0002] With recent revolutionary advances in electronic technologies,the integration of electronic circuits and the digitalization of signalprocessing have become common techniques. In such circumstances, theminiaturization/integration of continuous-time system filters essentialfor analog signal processing has been developed in the form of active RCfilters. In particular, the use of higher frequency bands beingaccelerated in line with recent digitalization requires taking up thechallenge of assuring high frequency characteristics. Therefore, signalprocessing in higher frequency bands has been developed to achieve highfrequency characteristics and high integration in active RC filters. Interms of noise problems involved in signal processing, continuous-timesystem filters also have advantage in intermediate or low frequencycharacteristics, and developments for achieving active RC filters usablein intermediate or low frequency bands and integration thereof have beenmade.

[0003] A second-order active circuit as a fundamental element of such anactive RC filter includes a Sallen-Key circuit using apositive-phase-sequence amplifier, a circuit using a single amplifierand a circuit using a gyrator.

[0004] In the Sallen-Key circuit, a positive feedback characteristic iscaused at the polar frequency (center frequency), and the sensitivity ofQ to variations in associated elements is extremely high. While thesingle-amplifier type circuit based on multiple-feedback can stablyachieve a high Q-value, it has a feed gain including the open loop gainof an operational amplifier at the polar frequency. While the transistorgyrator circuit can also stably obtain a high Q-value in a highfrequency range without difficulties, a positive feedback characteristicis caused at the polar frequency, and thus a desirable low-noiseperformance is hardly obtained.

[0005] As above, even though the conventional active RC filters based onthe second-order active circuits, such as the Sallen-Key circuit using apositive-phase-sequence amplifier, the single-amplifier type circuit andthe gyrator circuit, can conveniently obtain a high Q-values, all ofthem cannot maintain a negative feedback loop at the polar frequenciesof the second-order active circuit. Thus, these RC filters still involvea problem of difficulty in sufficiently reducing noises.

[0006] Due to the difficulty in striking a balance between high Q-valueand low noise performance in a high frequency range, any active RCfilter usable in a high frequency range has not been put to practicaluse up to now. In the practical design of filter circuits for use in ahigh frequency range, it has no choice but to employ an active coil(chip inductor) and externally combine it therewith. In particulate,this constitutes an adverse factor against achievement of small-sizedmonolithic ICs for use in a high frequency range.

[0007] Thus, there is still the need for facilitating integrationbetween various filter circuits including an inductance and othercircuits to provide downsized circuitries.

[0008] It is therefore an object of the present invention to provide anactive RC signal processing circuit having a transfer function capableof changing a negative feedback loop gain such that a transmission gainis reduced at a value equal to or less than a forward gain over theentire frequency range, to achieve a low noise characteristic.

DISCLOSURE OF INVENTION

[0009] In order to achieve the above object, the present inventionprovides a low-noise active RC signal processing circuit comprising afeedforward section operable responsive to an input signal to provide anoutput at a predetermined gain, and a feedback section operableresponsive to the output of the forward circuit to negatively feed backthe output to the input signal of the feedforward section while giving apredetermined transfer characteristic to the output, so as to allow theprocessing circuit to have a transfer impedance characteristic equal toor less than the predetermined gain over the entire frequency range.

[0010] In the above low-noise active RC signal processing circuit, thefeedforward section may be a current-controlled voltage output circuit.In this case, the current-controlled voltage output circuit may includea common-base transistor for receiving and inverting the input signal,and an emitter-follower transistor for outputting voltage, and may havea transfer impedance defining the predetermined gain. Alternatively, thecurrent-controlled voltage output circuit may include an operationalamplifier operable to invert the input signal, wherein the operationalamplifier is subjected to feedback according to the transfer impedancedefining the predetermined gain.

[0011] In the above low-noise active RC signal processing circuit, thefeedback section may be a multistage active RC circuit operable toprovide a frequency-dependent characteristic to the output from thefeedforward section. Alternatively, the feedback section may be avoltage-follower circuit operable to provide a frequency-dependentcharacteristic to the output from the feedforward section. Thevoltage-follower circuit may include an operational amplifier and amultistage RC circuit.

[0012] The low-noise active RC signal processing circuit may be abandpass filter, lowpass filter or highpass filter. In this case, thetransfer impedance characteristic defines the frequency characteristicof the filter.

BRIEF DESCRIPTION OF DRAWINGS

[0013]FIG. 1 is a basic block diagram showing a feedback type signalprocessing circuit of the present invention.

[0014]FIG. 2 is a basic block diagram showing a feedback type signalprocessing circuit according to a first embodiment of the presentinvention, wherein a transistor-based current controlled voltage sourceis used in a feedforward section.

[0015]FIG. 3 is a basic block diagram showing a second-order bandpassactive RC filter circuit according to the first embodiment.

[0016]FIG. 4 is a block diagram showing a specific example of thesecond-order bandpass active RC filter circuit in FIG. 3.

[0017]FIG. 5 is a graph showing a simulation result of thefrequency-transfer impedance characteristic of the second-order bandpassactive RC filter circuit in FIG. 4.

[0018]FIG. 6 is a block diagram showing another specific example of thesecond-order bandpass active RC filter circuit in FIG. 3, wherein theexample is configured in consideration of noise sources.

[0019]FIG. 7 is a graph showing the change of noise coefficient for loopgain.

[0020]FIG. 8 is a basic block diagram showing a second-order lowpassactive RC filter circuit according to the first embodiment.

[0021]FIG. 9 is a block diagram showing a specific example of thesecond-order lowpass active RC filter circuit in FIG. 8.

[0022]FIG. 10 is a graph showing a simulation result of thefrequency-transfer impedance characteristic of the second-order lowpassactive RC filter circuit in FIG. 9.

[0023]FIG. 11 is a basic block diagram showing a third-order lowpassactive RC filter circuit according to the first embodiment.

[0024]FIG. 12 is a basic block diagram showing another third-orderlowpass active RC filter circuit according to the first embodiment.

[0025]FIG. 13 is a block diagram showing a specific example of thethird-order lowpass active RC filter circuit in FIG. 12.

[0026]FIG. 14 is a graph showing a simulation result of thefrequency-transfer impedance characteristic of the third-order lowpassactive RC filter circuit in FIG. 13.

[0027]FIG. 15 is a basic block diagram showing a second-order highpassactive RC filter circuit according to the first embodiment.

[0028]FIG. 16 is a block diagram showing a specific example of thesecond-order highpass active RC filter circuit in FIG. 15.

[0029]FIG. 17 is a graph showing a simulation result of thefrequency-transfer impedance characteristic of the second-order highpassactive RC filter circuit in FIG. 16.

[0030]FIG. 18 is a basic block diagram showing a third-order highpassactive RC filter circuit modified from the second-order highpass activeRC filter circuit in FIG. 15.

[0031]FIG. 19 is a block diagram showing a specific example of thethird-order highpass active RC filter circuit in FIG. 18.

[0032]FIG. 20 is a graph showing a simulation result of thefrequency-transfer impedance characteristic of the third-order highpassactive RC filter circuit in FIG. 19.

[0033]FIG. 21 is an explanatory view of an OP-Amp-basednegative-phase-sequence current controlled voltage source.

[0034]FIG. 22 is a basic block diagram showing a second-order bandpassactive RC filter circuit according to a second embodiment of the presentinvention, wherein a negative-phase-sequence current controlled voltagesource is used in a feedforward section.

[0035]FIG. 23 is a graph showing a simulation result of thefrequency-transfer impedance characteristic of the second-order bandpassactive RC filter circuit in FIG. 22.

[0036]FIG. 24 is a block diagram a specific example of the second-orderbandpass active RC filter circuit in FIG. 22, wherein the example isconfigured to cancel the influence of a GB (Gain Band width) product.

[0037]FIG. 25 is a graph showing a simulation result of thefrequency-transfer impedance characteristic of the second-order bandpassactive RC filter circuit in FIG. 24.

[0038]FIG. 26 is a block diagram showing a second-order lowpass activeRC filter circuit according to the second embodiment

[0039]FIG. 27 is a graph showing a simulation result of thefrequency-transfer impedance characteristic of the second-order lowpassactive RC filter circuit in FIG. 26.

[0040]FIG. 28 is a block diagram showing a second-order highpass activeRC filter circuit according to the second embodiment

[0041]FIG. 29 is a graph showing a simulation result of thefrequency-transfer impedance characteristic of the second-order highpassactive RC filter circuit in FIG. 28.

[0042]FIG. 30 is a block diagram showing one modification of thesecond-order highpass active RC filter circuit in FIG. 28, wherein thecircuit is configured to eliminate the peak characteristic in FIG. 29.

[0043]FIG. 31 is a graph showing a simulation result of thefrequency-transfer impedance characteristic of the second-order highpassactive RC filter circuit in FIG. 30.

BEST MODE FOR CARRYING OUT THE INVENTION

[0044] With reference to the drawings, a low-noise active RC signalprocessing circuit of the present invention will now be described.

[0045] The fundamental principle of a negative feedback control forallowing a transmission gain to be reduced at a value equal to or lessthan a forward gain over the entire frequency range in the signalprocessing circuit of the present invention will be first described inconnection with FIG. 1.

[0046] The signal processing circuit of the present invention employs afeedback type active RC filter circuit. FIG. 1 is a block diagramshowing the feedback type circuit.

[0047] In FIG. 1, given that an input current is Ii, an output currentbeing Io, the transfer function of a feedforward section being T₁(s),and the transfer function of a feedback section being T₂(s),respectively. The input-output transfer function T(s) is expressed bythe following formula: $\begin{matrix}{{T(s)} = {{{Io}/{Ii}}\quad = {{T_{1}(s)}/\left\lbrack {1 - {{T_{1}(s)} \cdot {T_{2}(s)}}} \right\rbrack}}} & (1)\end{matrix}$

[0048] In order to allow the feedback type circuit in FIG to have anegative feedback characteristic such that a transmission gain isreduced at a value equal to or less than a forward gain, it is requiredto satisfy the following condition base on the input-output transferfunction T(s) in the formula (1):

∥T(s)∥=|T ₁(s)|  (2)

[0049] A desired filter characteristic can be achieved by selecting thetransfer functions T₁(s) and T₂(s) which satisfy the condition expressedby the formula (2).

[0050] However, it is difficult for the circuit in FIG. 1 to satisfy thecondition of the formula (2) in the entire frequency range including thepolar frequency. Thus, the function is transformed by introducing aconstant “a” (a>1) into the denominator of the input-output transferfunction T(s) in the formula (1). Consequently, the input-outputtransfer function T(s) in the formula (1) can be transformed as follows:$\begin{matrix}{{T(s)} = {{{T_{1}(s)}/{a\left\lbrack {1 - {{T_{1}(s)} \cdot {T_{2}(s)}}} \right\rbrack}}\quad = {{T_{1}(s)}/\left\lbrack {1 + a - 1 - {a\quad {{T_{1}(s)} \cdot {T_{2}(s)}}}} \right\rbrack}}} & (3)\end{matrix}$

[0051] Comparing between the respective input-output transfer functionsT(s) in the formulas (1) and (3), it is proved that the transferfunction T₂(s) of the feedback section in the formula (1) can bemodified into (1−a)/T₁(s)+aT₂(s), to obtain an input-output transferfunction T(s) satisfying the condition of the formula (2).

[0052] In the present invention, according to the principle based on theformula (2), the transfer functions T₁(s) and T₂(s) are selected suchthat a transmission gain is reduced at a value equal to or less than aforward gain over the entire frequency range, to construct a low-noiseactive RC signal processing circuit having a desired frequencycharacteristic.

[0053] The present invention will be described in more detail inconjunction with a first embodiment which uses abipolar-transistor-based current controlled voltage source (CCVS) in thefeedforward section, and a second embodiment which uses an OP-Amp-basednegative-phase-sequence CCVS, and specific examples thereof.

First Embodiment

[0054] None of the conventional Sallen-Key circuit, the multi-feedbacktype circuit and the gyrator circuit can achieve the circuit in FIG. 1satisfying the condition of the formula (2). In a first embodiment ofthe present invention, a bipolar-transistor-based CCVS is employed inthe feedforward section.

[0055] The transistor-based CCVS comprises a common-base transistorprovided on the input side, an emitter-follower transistor provided onthe output side, and a resistor R₁ connected between these transistors.Given that the input current and output voltage of the CCVS are Ii andVo, respectively, the relation Vo=R₁·Ii is satisfied, and the transferimpedance of the CCVS is R₁.

[0056] The transistor CCVS constructed as above capable of readilyproviding wideband characteristics is suitable for thehigh-frequency-compatible signal processing circuit of the presentinvention intended to obtain a desirable transmission gain over theentire frequency range. Further, the resistor serving as the transferimpedance allows T₁(s) as the numerator of the formula (2) to beconstant. Thus, only the transfer function in the denominator of theformula (2) can be selected to satisfy the condition of the formula (2)so as to obtain a desired frequency characteristic.

[0057]FIG. 2 is a basic block diagram showing a filter circuit which hasa feedforward section using a transistor-based CCVS, in accordance withthe feedback type circuit having the input-output transfer functionT(s). In this filter circuit, the transistor CCVS comprises acommon-base bipolar transistor Q₁, an emitter-follower bipolartransistor Q₂, and a resistor R₁, and forms the feedforward section ofthe feedback type active RC filter circuit. A feedback section isconnected between the input and output sides of the CCVS.

[0058] The basic block diagram in FIG. 2 shows only connections to theAC components of a signal, and omits any DC bias lines for driving thetransistors. All of after-mentioned basic block diagrams are illustratedin the same way.

[0059] In FIG. 2, given that each of the transistors used in the filtercircuit is an ideal transistor, the input-output transfer function T(s)of the circuit can be expressed by the following formula in the form oftransfer impedance: $\begin{matrix}{{T(s)} = {{{Vo}/{Ii}}\quad = {R_{1}/\left\lbrack {1 + {\left( {R_{1}/R_{E}} \right){\beta (s)}}} \right\rbrack}}} & (4)\end{matrix}$

[0060] , wherein β(s) is a transmission function of the feedbacksection.

[0061] This transmission function can be selected to provide a desiredfrequency characteristic, so that various filter circuits usable in ahigh frequency range can be achieved. Specific examples of thehigh-frequency-compatible low-noise signal processing circuit accordingto the first embodiment using the transistor CCVS will be described inmore detail in connection with various filter circuits, particularly, abandpass active RC filter, a lowpass active RC filter, and a highpassactive RC filter.

[0062] (Bandpass Active RC Filter Circuit)

[0063] An input-output transfer impedance function T(s) for allowing thefilter circuit in FIG. 2 to act as a second-order bandpass RC filter isgiven as the following formula:

T(s)=(R ₁ /Q)(s/ω ₀)/[1+(s/ω ₀)/Q+(s/ω ₀)²]  (5)

[0064] Given that T₁(jω₀)=R₁, the negative feedback amount of thefeedback section is increased to satisfy the inequality T(jω₀)<R₁,according to the condition of the formula (2).

[0065] Then, a constant “a” (a>1) is introduced into the denominator ofthe transfer impedance function T(s) of the formula (5) as follows:

T(s)=(R ₁ /Q)(s/ω ₀)/a[1+(s/ω ₀)/Q+(s/ω ₀)²]  (6)

[0066] Then, the formula (6) is transformed to obtain a transferimpedance function T(s) expressed by the following formula:

T(s)=R ₁/[1+a−1+aQ[(s/ω ₀)+(ω₀ /s)]  (7)

[0067] As seen from the formula (7), the decrease in level of atransmission gain is generated by the terms “a−1+aQ[(s/ω₀)+(ω₀/s)]” inthe denominator of the formula (7) or by changing the negative feedbackloop gain, independently of the gain of the feedforward section.

[0068] A transmission function β(s) for the formula (7) can be obtainedwith reference to the formula (5), as follows:

β(s)=(R _(E) /R ₁)[a−1+aQ{(s/ω ₀)+(ω₀ /s)}]  (8)

[0069] In this case,

T ₁(jω ₀)=R ₁/(1+a−1)  (9)

[0070] Further, when s=jω₀, an open loop gain is “1−a”.

[0071]FIG. 3 is a basic block diagram showing a second-order bandpassactive RC filter circuit based on the transmission function β(s) of theformula (8). In this filter circuit, a feedforward section comprises atransistor-based CCVS including transistors Q₁ and Q₂, and a resistorR₁, and a feedback section comprises transistors Q₃ to Q₆, capacitors C₁and C₂, and resistors R₂ to R₅ and R_(E). Given that each of thesetransistors is an ideal transistor, the transfer function of thesecond-order bandpass active RC filter circuit in FIG. 3 can beexpressed as follows:

T(s)=R ₁/[1+(R ₁ /R _(E))[R ₅ /R ₂ +sC ₂ R ₅+(R ₅ /R ₄)/(sC ₁ R₃)]  (10)

[0072] In this case, the angular frequency ω₀ at the center frequency ofthis filter circuit, and the Q-value can be calculated by the followingformulas:

ω₀=(C ₁ C ₂ R ₃ R ₄)^(−1/2)  (11)

Q=(C ₂ /C ₁)^(1/2) R ₅/(R₃ R ₄)^(1/2)(R _(E) /R ₁ +R ₅ /R ₂)  (12)

[0073] The loop gain “1−a” at the center frequency can also becalculated by the following formula:

1−a=−(R ₅ /R ₂)(R ₁ /R _(E))  (13)

[0074] As above, it is proved that the respective values of thecapacitors and resistors in the feedback section can be adjusted toconstruct a second-order bandpass active RC filter having a desiredfrequency characteristic. FIG. 4 is a block diagram showing a specificexample of the second-order bandpass active RC filter circuit. Thisblock diagram includes DC bias lines for driving transistors.

[0075] The second-order bandpass active RC filter circuit in FIG. 4 wasdesigned to achieve the targets of center frequency f₀=5 MHz andQ-value=10. In this filter circuit, 2SC3501 and 2SA1206 (available fromHITACHI) were used as NPN bipolar transistors and PNP bipolartransistors, respectively. The respective values of capacitors andresistors were set as follows:

[0076] C₁=10, C₂=60 (unit: pF)

[0077] R₁=3.5, R₂=10, R₃=0.7, R₄=1.5, R₅=2.3, R₆=4.4, R₇=5.1, R₈=0.6,

[0078] R₉=1.4, R_(E1)=0.1, R_(E2)=0.6 (unit: kO)

[0079] The transistors Q₈ and Q₉ in the second-order bandpass active RCfilter circuit in FIG. 4 were connected as compensating capacitance.

[0080]FIG. 5 shows a simulation result of the second-order bandpassactive RC filter circuit in FIG. 4, wherein the horizontal and verticalaxes represent frequency and the transfer impedance, respectively. As aresult, this filter circuit had a center frequency f₀=4.81 MHz, and aQ-value=8.15. According to the simulation data, |T(j|ω₀)| was about 1.6kO, which was less than the forward gain R₁=3.5 kO.

[0081] As seen from the simulation result in FIG. 5, the bandpass activeRC filter circuit has a high Q-value at the center frequency f₀.

[0082] The ability of facilitating noise reduction in the second-orderbandpass active RC filter circuit according to the above embodiment willbe described below on the assumption of specific noise sources.Specifically, respective noise sources of the transistors incorporatedin the second-order bandpass active RC filter circuit in FIG. 3 will bespecified, and noise output thereof will be calculated.

[0083]FIG. 6 shows a filter circuit configured in consideration of noisesources. Given that noise sources at the center frequency are voltagesources e_(nk), and current sources i_(nk), wherein k corresponds to thenumber of each of transistors. In FIG. 6, the bandpass active RC filtercircuit including the noise sources is configured in consideration of aDC bias constant current source Q₁₀.

[0084] As an example, noise outputs V_(ON)(e₃) and V_(ON)(i₃) caused,respectively, by the noise sources e_(n3) and i_(n3) concerning atransistor Q3 can be calculated by the following formulas:

|V _(ON)(e ₃)|=|T(j|ω ₀)·e _(n3) /R _(E)|  (14)

|V _(ON)(i ₃)|=|T(j|ω ₀)·i _(n3) R ₅ /R _(E)|  (15)

[0085] , wherein T(j|ω₀), ω₀ and Q-value are expressed as follows:

T(j|ω ₀)=R ₁/[1+(R ₅ /R ₂)(R ₁ /R _(E))]  (16)

ω₀=(C ₁ C ₂ R ₃ R ₄)^(−1/2)  (17)

Q=ω ₀ C ₂ R ₅(R ₁ /R _(E))/[1+(R ₅ /R ₂)(R ₁ /R _(E))]  (18)

[0086] Noise outputs V_(ON)(e_(k)) and V_(ON)(i_(k)) caused by theremaining noise sources e_(nk) and i_(nk) can be calculated in the sameway.

[0087] Then, the value a, or negative feedback loop gain “a−1”, can bechanged while maintaining each of the center frequency f₀ and theQ-value at a constant value, to calculate respective noise coefficientsN_(vk) for the voltage sources or the noise sources e_(nk), andrespective noise coefficients N_(Ik) for the current source or the noisesources i_(nk). The noise coefficients N_(vk), N_(Ik) are expressed asfollows:

N _(vk) =|V _(ON)(e _(k))/e _(nk)|  (19)

N _(Ik) =|V _(ON)(e _(k))/e _(nk)∥  (20)

[0088] In the filter circuit, the value of the resistor R₂ is adjustedto change the value a, and the respective values of the capacitor C₂ andthe resistor R₃ is adjusted to maintain the center frequency f₀ and theQ-value at a content value. Some examples in which the values of the RCelements are adjusted to change the value a in this manner will bedescribed below. R₂ 60 20 10 7 5 (kO) R₃ 1.24 0.93 0.7 0.56 0.47 (kO) C₂34 45 60 75 90 (pF) a 1.18 1.54 2.07 2.54 3.15 f₀ 5.00 5.02 5.01 5.015.00 (MHz) Q 10.31 10.37 10.11 10.28 9.84

[0089] The remaining RC elements other than the above RC elements arethe same as those of the filter circuit in FIG. 4. Further, a resistor Rin the input section is set at 3.5 kO, and R₁₀ is set at 0.9 kO. Acapacitor C₁ is set at 16 pF in consideration of the collectorcapacitances of transistors Q₄, Q₁₀ and Q_(5.)

[0090] The above values of the center frequencies f₀ and the Q-valueswere calculated by the formulas (17) and (18). Then, a noise coefficientfor the level of negative feedback loop gain “a−1” is calculated usingthe noise outputs calculated by the formulas (14) and (15). For example,the respective noise coefficients N_(V3), N_(I3) for the noise sourcese_(n3), i_(n3) can be calculated and plotted with respect to the noisecoefficient for the gain “a−1” to obtained the graph in FIG. 7, whereinFIG. 7(a) shows the relationship with the noise coefficient N_(V3) forthe noise source e_(n3), and FIG. 7(b) shows the relationship with thenoise coefficient N_(I3) for the noise source i_(n3). As can be seenfrom the relationship between the level “a−1” of the loop gain and eachof the noise coefficients N_(V3), N_(I3), the output noises can bereduced by designing the circuit such that the “a−1” is set at a largervalue, or the negative feedback loop amount is increased, and the outputnoise is at a fairly high level when no negative feedback is applied orwhen a=1. The relationships between the gain “a−1” and each of the noisecoefficients N_(Vk), N_(Ik) for the remaining noise sources e_(nk),i_(nk) exhibit the same tendencies as those in FIGS. 7(a) and 7(b), andthe related noise outputs are also reduced.

[0091] (Lowpass Active RC Filter Circuit)

[0092] An input-output transfer impedance function T(s) for allowing thefilter circuit in FIG. 2 to act as a second-order lowpass RC filter isgiven as the following formula:

T(s)=R ₁/[1+(s/ω _(P))/Q+(s/ω _(P))²]  (21)

[0093] This transfer function T(s) of the second-order lowpass RC filtercan be achieved by applying the following formula to the function β(s)in the formula (4):

β(s)=(R _(E) /R ₁)[(s/ω _(P))/Q+(s/ω _(P))²]  (22)

[0094] However, when s=jω_(P), |T(j|ω_(P))| is expressed as follows:

T(j|ω_(P))|=QR ₁  (23)

[0095] This means that |T(j|ω_(P))| will be greater than R1 or forwardgain, and the condition ∥T(s)∥<|T₁(s)| cannot be maintained. Thus, inorder to satisfy the condition T(s)∥<R1, the formula (21) can bemodified as follows:

T(s)=R ₁ /a[1+(s/ω _(P))/Q+(s/ω _(P))²]  (24)

[0096] , wherein a>1.

[0097] Using the formula (24), the level of a transmission gain can bereduced by adjusting the negative feedback loop gain, independently ofthe forward gain R₁/a. In the same manner as in the formula (7), thetransmission function β(s) of the negative feedback section can becalculated by the following formula:

β(s)=(R _(E) /R ₁)[a−1 +a(s/ω _(P))/Q+a(s/ω _(P))²]  (25)

[0098]FIG. 8 is a basic block diagram showing a second-order lowpassactive RC filter circuit having this transmission function β(s). In thisfilter circuit, a feedforward section comprises a transistor-base CCVSincluding transistors Q₁ and Q₂, and a resistor R₁ serving as a transferimpedance, and a feedback section including transistors Q₃ to Q₆,capacitors C₁ and C₂, and resistors R₂ to R₅ and R_(E).

[0099] Given that each of the transistors of the lowpass active RCfilter circuit in FIG. 8 is an ideal element, the transmission functionβ(s), polar angular frequency cop, Q-value and value “a” are expressedas follows:

β(s)=R ₅[1/R ₄ +sC ₁ R ₂(1/R ₃ +sC ₂)]  (26)

ω_(P)=[(R _(E) /R ₁ +R ₅ /R ₄)/(C ₁ C ₂ R ₂ R ₅)]^(1/2)  (27)

Q=[(C ₂ /C ₁)(R ₃ ² /R ₂ R ₅)(R _(E) /R ₁ +R ₅ /R ₄)]^(1/2)  (28)

a=1+(R ₁ /R _(E))(R ₅ /R ₄)  (29)

[0100]FIG. 9 is a block diagram showing a specific example of thesecond-order lowpass active RC filter circuit in FIG. 8. This examplewas designed to obtain a maximally flat characteristic, under thefollowing conditions:

Q ²=1/2

2(C ₂ /C ₁)(R ₃ ² /R ₂ R ₅)(R _(E) /R ₁ +R ₅ /R ₄)=1  (30)

[0101] In the second-order lowpass active RC filter circuit in FIG. 9,2SC3501 and 2SA1206 were used as NPN bipolar transistors and PNP bipolartransistors, respectively. The respective values of capacitors andresistors were set as follows:

[0102] C₁=C₂=35 (pF)

[0103] R₁=3.5, R₂=R₄=R₅=2, R₃=1.1, R₆=4.4, R₇=6.5, R₈=1.4, R₉=2.9,

[0104] R₁₀=0.3, R_(E)=2.5 (kO)

[0105] The second-order lowpass active RC filter circuit in FIG. 9 wasdesigned to achieve the targets of cutoff frequency fc=3 MHz and“a”=2.4. The transistors Q₈, Q₉, Q₁₀ and Q₁₁ were connected ascompensating capacitance.

[0106]FIG. 10 shows a simulation result of the second-order lowpassactive RC filter circuit designed to have the above values of theelements. As seen in FIG. 10, |T(j|ω₀)| is maintained below the forwardgain R1=3.5 kO in the entire frequency range. In particular, the filtercircuit exhibits a flat lowpass characteristic having an approximatelyconstant gain of about 1.4 kO in a frequency range of 3 MHz or less.

[0107] The second-order lowpass active RC filter circuit in FIG. 8 canbe extended to provide a higher-order filter circuit. FIG. 11 is a basicblock diagram showing a lowpass active RC filter circuit extended tothird order.

[0108] Specifically, the second-order lowpass active RC filter circuitin FIG. 8 is extended to a higher-order lowpass active RC filter circuitby providing a multistage-circuitry corresponding to the transmissionfunction β(s) in the feedback section of the filter circuit in FIG. 8.The filter circuit in FIG. 11 is extended to third order by providing atwo-stage circuitry related to the transmission function β(s). If theimperfection of transistors (collector capacitance or the like) is leftout of consideration, the transfer function T(s) of the filter circuitcan be expressed as follows: $\begin{matrix}{{T(s)} = {{{Vo}/{Ii}}\quad = {R_{1}/\left\lbrack {1 + {\left( {R_{1}{R_{7}/R_{E}}} \right)\left( {{1/R_{3}} + \quad {{sC}_{1}{R_{2}/R_{5}}} + {s^{2}C_{1}C_{2}R_{2}{R_{4}/R_{6}}} + {s^{3}C_{1}C_{2}C_{3}R_{2}R_{4}}} \right)}} \right\rbrack}}} & (31)\end{matrix}$

[0109] The feedback section related to β(s) in the above third-orderlowpass active RC filter circuit includes feedback resistor elements R₃,R₅ and R₆ which are connected to the emitter of a transistor Q₈ in aconcentrated manner. While the basic block diagram in FIG. 11 isillustrated with a focus only on the AC components of a signal, and anyDC bias lines are omitted therein, the feedback resistors connected tothe emitter of a transistor Q₈ in a concentrated manner makes itdifficult to layout the DC bias line in a practical circuit design.

[0110]FIG. 12 is a basic block diagram showing another third-orderlowpass active RC filter circuit designed to prevent a plurality offeedback resistor elements from being connected to the emitter of thetransistor Q₈ in a concentrated manner. In this filter circuit, insteadof connecting feedback resistor elements R₂, R₄ and R₆ from the emitterof the transistor Q₈ to respective input sides in the feedback sectionrelated to β(s), they are connected from respective output sides torespective input sides in the feedback section related to β(s) or to theoutput side of the filter circuit, to allow the bias line for theemitter of the transistor Q₈ to be designed without difficulties.

[0111] The feedback section of this third-order lowpass active RC filtercircuit has the following transmission function β(s):

β(s)=[(1/R ₂ +sC ₁)sC ₂ R ₃+1/R ₄ ]sC ₃ R ₅+1/R ₆  (32)

[0112] , and the transfer function T(s) of the filter circuit isexpressed as follows: $\begin{matrix}{{T(s)} = {{{Vo}/{Ii}}\quad = {R_{1}/\left\lbrack {1 + {\left( {R_{1}{R_{7}/R_{E}}} \right)\left( {{1/R_{6}} + \quad {{sC}_{3}{R_{5}/R_{4}}} + {s^{2}C_{2}C_{3}R_{3}{R_{5}/R_{2}}} + {s^{3}C_{1}C_{2}C_{3}R_{3}R_{5}}} \right)}} \right\rbrack}}} & (33)\end{matrix}$

[0113] Given that a passband ripple a_(P)=0.5 dB, the transfer functionT(s) of the third-order lowpass active RC filter circuit having aforward gain R₁ can be calculated as follows:

T(s)=R₁/[1+2.144625(jω/ωc)+1.750624313(jω/ωc)²+1.39724329(jω/ωc)³]  (34)

[0114]FIG. 13 shows a specific example of this third-order lowpassactive RC filter circuit. Various elements of this filter circuit weredesigned to achieve the targets of “a”=3 and cutoff frequency fc=5 MHz.In this filter circuit, 2SA1206 and 2SC3501 were used as PNP bipolartransistors and NPN bipolar transistors, respectively. The respectivevalues of elements were set as follows:

[0115] Capacitor C₁=15, C₂=C₃=40, Cs=1 (pF)

[0116] Resistor R₁=3.5, R₂=2, R₃=0.8, R₄=1.9, R₅=2.7, R₆=2.1, R₇=3,R₈=1, R₉=6.4, R₁₀=2.3, R₁₁=6.4, R₁₂=5, R₁₃=4.4, R_(E)=2.5 (kO)

[0117] The collector capacitance of each pair of parallel transistorsQ₁₀ and Q₁₁, Q₁₂ and Q₁₃, Q₁₄ and Q₁₅, and Q₁₆ and Q₁₇ acts to canceland compensate the collector capacitance of each pair of paralleltransistors Q₄ and Q₅, Q₆ and Q₇, Q₈ and Q₃, and Q₁ and Q₂.

[0118]FIG. 14 shows a simulation result of the frequency-transferimpedance characteristic of the lowpass active RC filter circuit in FIG.13. As seen in the result, the transfer impedance in a low frequencyrange is about 1.2 kO, or attenuated to 1/a of the forward gain R1=3.5kO by the negative feedback. Further, the result clearly shows that thenegative feedback is sufficiently applied over the entire frequencyrange.

[0119] While the simulation result in FIG. 14 was performed on theassumption of a temperature Ta=270° C., the same frequency-transferimpedance characteristic could also be obtained in the temperature rangeof 0 to 80° C. This shows that the filter circuit has stablecharacteristics to variation in temperature.

[0120] In the same manner as that described in connection with FIG. 6,noise coefficients N_(Vk), N_(IK) for the level of loop gain “a−1” couldbe calculated, and it was verified that an improved low-noiseperformance can be obtained by increasing the loop gain “a−1”.

[0121] (Highpass Active RC Filter Circuit)

[0122] An input-output transfer impedance function T(s) for allowing thefilter circuit in FIG. 2 to act as a second-order highpass RC filter isgiven as the following formula:

T(s)=1/[1+(ω_(P) /s)Q+(ω_(P) /s)²]  (35)

[0123] However, considering a feedback loop for achieving this transferfunction, when Q>1 in the formula (35), |T(j|ω_(P))| becomes greaterthan 1 or the forward gain=1, and cannot satisfy the condition of theformula (2). Since this transfer function cannot achieve adequatenegative feedback without modification, a constant “a” (a>1) isintroduced into the denominator of the formula (35) to modify theformula (35) as follows: $\begin{matrix}{{T(s)} = {{1/{a\left\lbrack {1 + {\left( {\omega_{P}/s} \right)/Q} + \left( {\omega_{P}/s} \right)^{2}} \right\rbrack}}\quad = {1/\left\lbrack {1 + a - 1 + {{a\left( {\omega_{P}/s} \right)}/Q} + {a\left( {\omega_{P}/s} \right)}^{2}} \right\rbrack}}} & (36)\end{matrix}$

[0124] Then, the level of a transmission gain of the filter circuit willbe reduced by adjusting the negative feedback loop gain“a−1+a(ω_(P)/s)/Q+a(ω_(P)/s)²”, independently of the forward gain.

[0125]FIG. 15 is a basic block diagram showing a second-order highpassactive RC filter circuit which comprises a feedforward section employingthe aforementioned transistor-based CCVS, and a feedback section capableof obtaining the feedback loop gain in the formula (36). Thetransistor-based CCVS includes transistor Q₁ and Q₂, a resistor R₁. Thefeedback section includes transistors Q₃ to Q₈, capacitors C₁ and C₂,and resistors R₂ to R₇ and R_(E).

[0126] The transmission function β(s) of the negative feedback sectionin this second-order highpass active RC filter circuit can be calculatedby the following formula:

β(s)=(R _(E) /R ₁)[a -1 +a(ω_(P) /s)/Q+a(ω_(P) /s)²]  (37)

[0127] Given that each of the transistors used in the filter circuit isan ideal element, the transfer function T(s) for the formula (36) isgiven as follows:

T(s)=R ₁/[1+(R ₁ /R ₂)(R ₇ /R _(E))+(R ₁ R ₄ /s ³ C ₂ R ₃ R ₅ R ₆)(R ₇/R _(E))+(R ₁ /s ² C ₁ R ₃ R ₅ R ₆)(R ₇ /R _(E))]  (38)

[0128] , and polar angular frequency ω_(P), Q-value and value “a” areexpressed as follows:

ω_(P) ²=(R ₁ /C ₁ C ₂ R ₃ R ₅ R ₆)/(R ₁ /R ₂ +R _(E) /R ₇)  (39)

Q ²=[(C ₂ /C ₁)(R ₃ R ₅ R ₆ /R ₁ R ₄ ²)(R ₁ /R ₂ +R _(E) /R ₇)  (40)

a=1+(R ₁ /R ₂)(R ₇ /R _(E))  (41)

[0129]FIG. 16 shows a specific example of the highpass active RC filtercircuit in FIG. 15, wherein DC bias lines are includes. This example wasdesigned to obtain a maximally flat characteristic, under the followingconditions:

Q ²=1/2

2(C ₂ /C ₁)R ₃ R ₅ R ₆ /R ₁ R ₄ ²)(R ₁ /R ₂ +R _(E) /R ₇)=1  (42)

[0130] In this filter circuit in FIG. 9, 2SC3501 and 2SA1206 were usedas NPN bipolar transistors and PNP bipolar transistors, respectively.The respective values of elements were set as follows:

[0131] Capacitor C₁=234, C₂=240 (pF)

[0132] Resistor R₁=R₄=3.2, R₂=R₃=R₉=R₁₁=0.6, R₅=2.6, R₆=1.4, R₇=0.8,R₈=R₁₀=2.2, R₁₂=R₁₄=1.2, R₁₃=R₁₅=3.8, R_(E)=1.0 (kO)

[0133]FIG. 17 shows a simulation result of the frequency-transferimpedance characteristic of the highpass active RC filter circuit inFIG. 16. In this figure, while the transfer impedance is reduced in 100MHz or more, this is caused by high-frequency characteristics of thetransistors themselves. Further, the characteristic indicated by adotted line is caused by the influence of parasitic transistors. Inorder to eliminate this influence, the highpass active RC filter circuitin FIG. 16 includes a capacitor Cs (3.5 pF) inserted into the emitter ofa transistor Q₃. The characteristic after inserting the capacitor Cs isshown by the solid line in FIG. 17. This curve shows that the highpassactive RC filter circuit has a flat characteristic.

[0134] In the same manner as that described in connection with FIG. 6,noise coefficients N_(Vk), N_(IK) for the level of loop gain “a−1” couldbe calculated, and it was verified that an improved low-noiseperformance can be obtained by increasing the loop gain “a−1”.

[0135] An example in which the second-order highpass active RC filtercircuit in FIG. 15 is extended to higher order will be described below.This higher-order highpass active RC filter circuit can be obtained inthe same manner as that in the aforementioned lowpass active RC filtercircuit, and the transfer impedance function β(s) in the formula (37)can be achieved by providing a multistage-connection of integrationcircuits in the feedback section of the highpass active RC filtercircuit.

[0136] As an example, FIG. 18 is a basic block diagram showing athird-order highpass active RC filter circuit obtained by extending thesecond-order highpass active RC filter circuit. In the third-orderhighpass active RC filter circuit, feedback resistors R₄, R₆ and R₈ isarranged such that they are not connected to a transistor Q₁₀ in aconcentrated manner. The reason is the same as that in theaforementioned lowpass active RC filter circuit.

[0137] The transfer function T(s) of the third-order highpass active RCfilter circuit can be calculated by the following formula:$\begin{matrix}{{T(s)} = {{{Vo}/{Ii}}\quad = {R_{1}/\left\lbrack {1 + {\left( {R_{1}{R_{9}/R_{E}}} \right)\left\{ {{{\left( {{{1/S^{2}}C_{1}C_{2}R_{2}R_{3}R_{5}} + \quad {{1/s}\quad C_{2}R_{4}R_{5}} + {1/R_{6}}} \right)/s}\quad C_{3}R_{7}} + {1/R_{8}}} \right\}}} \right\rbrack}}} & (43)\end{matrix}$

[0138] Given that a passband ripple a_(P)=0.5 dB, the transfer functionT(s) of the third-order highpass active RC filter circuit having aforward gain R₁ can be calculated as follows:

T(s)=R₁/[1.39724329(ωc/jω)³+1.750624313(ωc/jω)²+2.144625(ωc/jω)+1]  (44)

[0139]FIG. 19 shows a specific example of the third-order highpassactive RC filter circuit in FIG. 18. Various elements of this filtercircuit were designed to achieve the targets of “a”=4 and cutofffrequency fc=300 kHz. In this filter circuit, 2SA1206 and 2SC3501 wereused as PNP bipolar transistors and NPN bipolar transistors,respectively. The respective values of elements were set as follows:

[0140] Capacitor C₁=C₂=C₃=90, Cs=1 (pF)

[0141] Resistor R₁=R₂=3.5, R₃=3.4, R₄=R₁₅=1.9, R₅=3, R₆=0.9, R₇=2, R₈=1,R₉=2.2, R₁₀=4.4, R₁₁=1.2, R₁₂=R₁₃=0.6, R₁₄=3.2, R₁₅=1.8, R₁₆=1.4,R_(E)=2.5 (kO)

[0142] Each of transistors Q₁₅ and Q₁₆, Q₁₇ and Q₁₈, Q₁₉ and Q₂₀, andQ₂₁ acts as compensating capacitance to cancel the collector capacitanceof each of transistors Q₄ and Q₅, Q₆ and Q₇, Q₈ and Q₉, and Q₁₀ and Q₃.

[0143]FIG. 20 shows a simulation result of the frequency-transferimpedance characteristic of the third-order highpass active RC filtercircuit in FIG. 19. The resistor Rs (40 kO) connected in parallel withthe capacitor C₂ can suppress the peak in a low frequency range asindicated by the dotted line in FIG. 20 to provide a third-orderhighpass active RC filter circuit having a flat frequency-transferimpedance characteristic as indicated by the solid line. The attenuationin a high frequency range in this characteristic is caused byhigh-frequency characteristics of the transistors themselves.

[0144] As seen in the result, the transfer impedance in a low frequencyrange is about 1.2 kO, or attenuated to 1/a of the forward gain R1=3.5kO by the negative feedback. Further, the result clearly shows that thenegative feedback is sufficiently applied over the entire frequencyrange.

Second Embodiment

[0145] In the first embodiment, the filter circuit comprises thefeedforward section employing the transistor-based CCVS, and thefeedback section, wherein the transfer impedance function of thefeedback section allowing the transfer function of the filter circuit tosatisfy the formula (2) is selected to change a negative feedback loopgain such that a transmission gain is reduced at a value equal to orless than a forward gain over the entire frequency range.

[0146] In a second embodiment, an op-amp-based negative-phase-sequenceCCVS is used as a substitute for the transistor-based CCVS, and anegative feedback loop gain is changed such that a transmission gain isreduced at a value equal to or less than a forward gain over the entirefrequency range. Further, the loop gain is increased over the entirefrequency range to facilitate noise reduction in a signal processingcircuit.

[0147]FIG. 21(a) shows the structure of an op-amp-basednegative-phase-sequence CCVS. Fundamentally, the negative-phase sequenceCCVS comprises an operational amplifier OP₁, and a resistor R₁ connectedbetween the inverting input side and the output side of the operationalamplifier OP₁. If the finite GB product of the operational amplifier OP₁is left out of consideration, an equivalent circuit as shown in FIG.21(b) can be obtained. An input signal is supplied to the invertinginput of the operational amplifier OP₁, and thus a corresponding outputhas a reverse phase to that of the input signal, and the resistor R₁serves as an impedance for current-voltage conversion. The operationalamplifier can be composed of a MOS transistor.

[0148] An active RC filter circuit provided using an op-amp-basednegative-phase-sequence CCVS and having a transfer function to bechanged such that it a transmission gain is reduced at a value equal toor less than a forward gain while satisfying the aforementioned formula(2) to provide a desired frequency characteristic will be describedbelow in connection with respective examples of a bandpass filtercircuit, a lowpass filter circuit and a highpass filter circuit.

[0149] (Bandpass Active RC Filter Circuit)

[0150]FIG. 22 shows a negative-feedback type second-order bandpassactive RC filter circuit using an op-amp-based negative-phase-sequenceCCVS. The circuit in FIG. 21(a) is directly used as thenegative-phase-sequence CCVS. The filter circuit comprises a negativefeedback section connected between the input and output sides of thenegative-phase-sequence CCVS. The negative feedback section includesoperational amplifiers OP₂ and OP₃, capacitors C₁ and C₂, and resistorsR₂ to R₅.

[0151] Given that each of the operational amplifiers OP₁ to OP₃ are anideal element with disregard to the finite GB product thereof, thetransfer impedance function Z_(T) is Vo/Ii. Thus, the following formulacan be obtained:

Z _(T) =−R ₁/[1+R ₁(sC ₁ +R ₃ /sC ₂ R ₂ R ₄ R ₅)]  (45)

[0152] The center angular frequency ω₀ and Q-value are also obtained asfollows:

ω₀=(R ₃ /C ₁ C ₂ R ₂ R ₄ R ₅)^(1/2)  (46) $\begin{matrix}{Q = {{R_{1}\left( {C_{1}{R_{3}/C_{2}}R_{2}R_{4}R_{5}} \right)}_{\frac{1}{2}} = {\omega_{0}R_{1}C_{1}}}} & (47)\end{matrix}$

[0153] The characteristic of the second-order bandpass active RC filtercircuit in FIG. 22 was simulated by assigning specific numerical valuesto the elements thereof. FIG. 23 shows a frequency-transfer impedancecharacteristic obtained as a simulation result. The filter circuit wasdesigned to achieve the targets of center frequency f₀=100 kHz andQ-value=10. LF 356 (GB=5 MHz: available from National SemiconductorCorp.) was used as the operational amplifiers. The values of thecapacitors and registers were set as follows:

[0154] C₁=100, C₂=10 (pF)

[0155] R₁=150, R₂=R₃=R₄=R₅=50 (kO)

[0156] In FIG. 23 as the simulation result, the filter circuit has acenter frequency f₀=94 kHz, and a Q-value=21. The deviation between thetarget value and the result is caused by the finite GB product of theoperational amplifiers.

[0157] As apparent from the formula (46), no negative feedback is formedeven at the center frequency f₀. Further, as seen in FIG. 23, thetransfer impedance at the center frequency f₀ is about 350 kO, which isfar greater than R₁=150 kO. This means that the second-order bandpassactive RC filter circuit in FIG. 22 cannot satisfy the condition of theformula (2), or cannot maintain negative feedback at the centerfrequency f₀, without modification.

[0158]FIG. 24 shows a modified second-order bandpass active RC filtercircuit capable of increasing a negative feedback amount to satisfy theconditions of the formula (2) over the entire frequency range includingthe center frequency f₀ so as to facilitate the reduction of gain level.The second-order bandpass active RC filter circuit in FIG. 24 has thesame fundamental structure as that of the filter circuit in FIG. 22,except for a resistor R₅ inserted in series with the capacitor C₂ in thefeedback section of the operational amplifier P₃, and a resistor Rsconnected in series with the capacitor C₁, and a capacitor Cs connectedin parallel with the resistor R₆.

[0159] Given that each of the operational amplifiers OP₁ to OP₃ is anideal element, the transfer impedance function Z_(T) of the filtercircuit is expressed as follows: $\begin{matrix}{Z_{T} = {\frac{V_{0}}{I_{i}} = \frac{R_{1}}{\quad {\left( {1 + {R_{1} \cdot \frac{R_{3}}{R_{2}} \cdot \frac{R_{5}}{R_{4}R_{6}}}} \right) \cdot {\quad\left\lbrack {1 + {\frac{R_{1}}{1 + {R_{1} \cdot \frac{R_{3}}{R_{2}} \cdot \frac{R_{5}}{R_{4}R_{6}}}} \cdot \left( {{sC}_{1} + {\frac{1}{{sC}_{2}} \cdot \frac{R_{3}}{R_{2}} \cdot \frac{1}{R_{4}R_{6}}}} \right)}} \right\rbrack}}}}} & (48)\end{matrix}$

[0160] In this case, the constant “a” is expressed as follows:$\begin{matrix}{a = {1 + {R_{1} \cdot \frac{R_{3}}{R_{2}} \cdot \frac{R_{5}}{R_{4}R_{6}}}}} & (49)\end{matrix}$

[0161] Further, the center angular frequency ω₀ and the Q-value areexpressed as follows: $\begin{matrix}{\omega_{0} = \sqrt{\frac{R_{3}}{C_{1}C_{2}R_{2}R_{4}R_{6}}}} & (50) \\{Q = {\frac{R_{1}}{{R_{2}R_{4}R_{6}} + {R_{1}R_{3}R_{5}}}\sqrt{\frac{C_{1}R_{2}R_{3}R_{4}R_{6}}{C_{2}}}}} & (51)\end{matrix}$

[0162] The transfer impedance Z_(T) of the filter circuit determinedbased on the formula (48) by taking account of the respective finite GBproducts GB₁ to GB₃ of the operational amplifiers OP₁ to OP₃ isexpressed as follows: $\begin{matrix}\begin{matrix}{Z_{T} = \frac{V_{0}}{I_{i}}} \\{= {- \frac{R_{1}}{1 + {\left( {1 + \frac{R_{1}}{R_{6}}} \right)\frac{s}{{GB}_{1}}} + {\frac{{sC}_{1}R_{1}}{1 + {{sC}_{1}R_{5}}}\left( {1 + \frac{s}{{GB}_{1}}} \right)} + \frac{{\frac{R_{3}}{R_{2}} \cdot \frac{R_{1}\left( {1 + {{sC}_{5}R_{6}}} \right)}{R_{6}}}\left( {\frac{R_{5}}{R_{4}} + \frac{1}{{sC}_{2}R_{4}}} \right)}{\left\lbrack {1 + {\frac{s}{{GB}_{2}}\left( {1 + \frac{R_{3}}{R_{2}}} \right)}} \right\rbrack \cdot \left\lbrack {1 + {\frac{s}{{GB}_{3}}\left( {1 + \frac{R_{5}}{R_{4}} + \frac{1}{{sC}_{2}R_{4}}} \right)}} \right\rbrack}}}}\end{matrix} & (52)\end{matrix}$

[0163] The resistor Rs and the capacitor Cs are used as compensatingelements for cancelling the influence of the GB products.

[0164] With the targets of “a”=2.2, center frequency f₀=100 kHz andQ-value=10, the characteristic of the filter circuit was simulated byassigning the following values to the elements.

[0165] Capacitor C₁=150, C₂=85, Cs=1 (pF)

[0166] Resistor R₁=200, R₂=10, R₃=150, R₄=R₆=50, R₅=1 (kO), Rs=80 O

[0167] LF 357 (GB=15 MHz: available from National Semiconductor Corp.)was used as the operational amplifiers OP₁ to OP₃.

[0168]FIG. 25 shows a simulation result of the frequency-transferimpedance characteristic of the second-order bandpass active RC filtercircuit having the elements arranged as above. According to this result,the filter circuit has a center frequency F₀=109 kHz and a Q-value=9.5which well match with the targets. Further, the transfer impedance atcenter frequency F₀ is about 95 kO which is less than the transferimpedance R₁=200 kO of the feedforward section. This shows that thesecond-order bandpass active RC filter circuit in FIG. 24 satisfies thecondition of the formula (2), and the negative feedback is sufficientlyapplied thereto over the entire frequency range.

[0169] (Lowpass Active RC Filter Circuit)

[0170] A conventional lowpass filter using bipolar transistors hasemployed a multistage differentiation circuit in a feedback sectionthereof. In a second-order lowpass active RC filter circuit using anegative-phase-sequence CCVS based on an operational amplifier OP₁, afrequency-dependent voltage follower composed of an operationalamplifier and a multistage-RC integration circuit is used in a feedbacksection.

[0171]FIG. 26 shows the structure of the above second-order lowpassactive RC filter circuit. In this filter circuit, thenegative-phase-sequence CCVS based on the operational amplifier OP₁ isinterposed between the input and output of a feedforward sectionthereof, and the multistage-RC integration circuit including capacitorsC₁, C₂, and resistor R₂, R₃ is connected between the inverting inputside and the output side of an operational amplifier OP₂ in a feedbacksection thereof.

[0172] Given that each of the operational amplifiers is an idealelement, the output voltage V of the operational amplifier OP₂ isexpressed as follows:

V=Vo[(R ₂ +R ₃ +R ₄)/R ₄ +s[C ₂(R ₂ +R ₃)+C ₁(R ₃ +R ₄)(R ₂/R₄)]+s ² C ₁C ₂ R ₂ R ₃]  (53)

[0173] As seen from the formula (53), it is noted that the multistageladder connection composed of the capacitors C₁, C₂, and resistor R₂, R₃in FIG. 26 provides an “s” polynomial equation for feedbacktransmission.

[0174] The transfer impedance function Z_(T) of the second-order lowpassactive RC filter circuit in FIG. 26 is expressed as follows:$\begin{matrix}\begin{matrix}{Z_{T} = \frac{V_{0}}{I_{i}}} \\{= \frac{R_{1}}{1 + {\frac{R_{1}}{R_{5}} \cdot \frac{R_{2} + R_{3} + R_{4}}{R_{5}}} + {s{\frac{R_{1}}{R_{5}}\left\lbrack {{C_{2}\left( {R_{2} + R_{3}} \right)} + {\frac{C_{1}R_{2}}{R_{4}}\left( {R_{3} + R_{4}} \right)}} \right\rbrack}} + {s^{2}\frac{C_{1}C_{2}R_{1}R_{2}R_{3}}{R_{5}}}}}\end{matrix} & (54)\end{matrix}$

[0175] The constant “a”, the center angular frequency ω₀ and the Q-valueare expressed as follows: $\begin{matrix}{a = {1 + {\frac{R_{1}}{R_{5}} \cdot \frac{R_{2} + R_{3} + R_{4}}{R_{4}}}}} & (55) \\{\omega_{P} = \sqrt{\frac{1 + \frac{R_{2} + R_{3}}{R_{4}} + \frac{R_{5}}{R_{1}}}{C_{1}C_{2}R_{2}R_{3}}}} & (56) \\{Q = \frac{\sqrt{C_{1}C_{2}R_{2}{R_{3}\left( {1 + \frac{R_{5}}{R_{1}} + \frac{R_{2} + R_{3}}{R_{4}}} \right)}}}{{C_{2}\left( {R_{2} + R_{3}} \right)} + {C_{1}{R_{2}\left( {1 + \frac{R_{3}}{R_{4}}} \right)}}}} & (57)\end{matrix}$

[0176] The transfer impedance function Z_(T)(s) of the second-orderlowpass active RC filter circuit determined based on the formula (54) bytaking account of the respective finite GB products GB₁ to GB₃ of theoperational amplifiers OP₁ to OP₃ is expressed as follows:

Z _(T)(s)=−R ₁/[1+s/GB ₁(1+R ₁ /R ₅)+(R₁ /R ₅)/(A+s/GB ₂)]  (58)

[0177] , wherein

A=1/[1+(R ₂ +R ₃)/R ₄ +s[(R ₁ +R ₃)C ₃ +R ₂ R ₃ C ₂ /R ₄ ]+s ² C ₂ C ₃ R₂ R ₃]  (59)

[0178] With the targets of “a”=1.6, cutoff frequency f_(P)=100 kHz andQ-value=0.72, the characteristic of the second-order lowpass active RCfilter circuit in FIG. 26 was simulated by assigning the followingvalues to the elements.

[0179] Capacitor C₁=C₂=195 (pF)

[0180] Resistor R₁=50, R₂=R₃=25, R₄=20, R5=300 (kO)

[0181]FIG. 27(a) shows a simulation result of the frequency-transferimpedance characteristic of the second-order lowpass active RC filtercircuit having the elements arranged as above. According to this result,while the filter circuit has a transfer impedance less than 50 kO in alow frequency range, and a cutoff frequency of 105 kHz which are closeto the targets, a large peak occurs at a high frequency of 16 MHz.Because the differential and integral calculus of s/GB₁(1+R₁/R₅)″ and(R₁/R₅)/(A+s/GB₂) in the denominator of the formula (58) causes a peakcharacteristic in an extremely high frequency region

[0182] In order to prevent any peak characteristic from occurring insuch a high frequency range, a capacitance Cs is connected in parallelwith the resistor R₅ provided in the feedback section of thesecond-order lowpass active RC filter circuit in FIG. 26. The capacitorCs primarily acts to compensate the GB₂ of the operational amplifierOP₂.

[0183] After connecting the capacitor Cs (5 pF) to the resistor R₅, thecharacteristic of the filter circuit having the elements arranged asdescribed above was simulated. As a result, the frequency-transferimpedance characteristic as shown in FIG. 27(b) could be obtained. Thisresult shows that the Q-value is increased up to 1.18 through thecompensation of the GB₂, and the above targets are achieved.

[0184] (Highpass Active Filter Circuit)

[0185]FIG. 28 shows a second-order highpass active RC filter circuitusing an op-amp-based negative-phase-sequence CCVS. The filter circuitcomprises a feedforward section which includes a negative-phase-sequenceCCVS based on an operational amplifier OP₁, and a feedback section whichincludes a frequency-dependent voltage follower composed of anoperational amplifier OP₂ and a two-stage differentiation circuit havingcapacitors C₁, C₂, and resistor R₂, R₃. A higher-order highpass filtercan be obtained by increasing the number of stages of the RCdifferentiation circuit. It is noted that this differentiation circuitprovides a (1/s) polynomial equation for feedback transmission.

[0186] Given that each of the operational amplifiers is an idealelement, the transfer impedance function Z_(T)(s) of the second-orderhighpass active RC filter circuit in FIG. 28 is expressed as follows:$\begin{matrix}{Z_{T} = \frac{R_{1}}{1 + {\frac{R_{1}}{R_{4}} \cdot {\frac{R_{1}}{R_{4}}\left\lbrack {\frac{{\left( {C_{1} + C_{2}} \right)R_{2}} + {C_{2}R_{3}}}{{sC}_{1}C_{2}R_{2}R_{3}} + \frac{1}{s^{2}C_{1}C_{2}R_{2}R_{3}}} \right\rbrack}}}} & (60)\end{matrix}$

[0187] The constant “a”, the center angular frequency ω₀ and the Q-valueare expressed as follows: $\begin{matrix}{a = {1 + \frac{R_{1}}{R_{4}}}} & (61) \\{\omega_{P} = \frac{1}{\sqrt{\left( {1 + {\frac{R_{1}}{R_{4}}C_{1}C_{2}R_{2}R_{3}}} \right)}}} & (62) \\{Q = \frac{\sqrt{\left( {1 + \frac{R_{1}}{R_{4}}} \right)}C_{1}C_{2}R_{2}R_{3}}{\frac{R_{1}}{R_{4}}\left\lbrack {{\left( {C_{1} + C_{2}} \right)R_{2}} + {C_{2}R_{3}}} \right\rbrack}} & (63)\end{matrix}$

[0188] With the targets of “a”=1.5, cutoff frequency f₀=175 kHz andQ-value=0.8, the characteristic of the second-order highpass active RCfilter circuit in FIG. 28 was simulated by assigning the followingvalues to the elements.

[0189] Capacitor C₁=C₂=30 (pF)

[0190] Resistor R₁=50, R₂=R₃=25, R₄=100 (kO)

[0191]FIG. 29 shows a simulation result of the frequency-transferimpedance characteristic of the second-order highpass active RC filtercircuit having the elements arranged as above. According to this result,as with the lowpass active RC filter circuit, a peak characteristic isexhibited at a high frequency of 18 MHz.

[0192] Thus, the transfer impedance function Z_(T)(s) of the filtercircuit determined based on the formula (60) by taking account of theinfluence of the finite GB products of the operation amplifiers isexpressed as follows:

Z _(T)(S)=−R ₁/[1+s/GB ₁(1+R ₁ /R ₄)+(R ₁ /R ₄)/(A+s/GB ₂)]  (64)

[0193] , wherein

A=1/[(C₁ +C ₂)R ₂ +C ₂ R ₃)/sC ₁ C ₂ R ₂ R ₃+1/s ² C ₁ C ₂ R ₂ R ₃  (65)

[0194] As seen in these formulas, when the angular frequency ω is closeto GB₁, GB₂, the “A” in the formula (65) can be negligible, and a peakcharacteristic is controlled by s/GB₁(1+R₁/R₄) and (R₁/R₄)/(A+s/GB₂).Thus, a capacitance Cs is connected in parallel with the resistor R₄ tocompensate such a peak characteristic. FIG. 30 shows a modified circuitobtained by connecting the compensating capacitor Cs to the second-orderhighpass active RC filter circuit.

[0195] The characteristic of the filter circuit having the capacitor Cs(0.3 pF) to the resistor R₄ was simulated by assigning the above valuesto the elements, and the result is shown in FIG. 31 as afrequency-transfer impedance characteristic. This result shows that apeak characteristic is desirably improved in a high frequency range bythe capacitor Cs.

INDUSTRIAL APPLICABILITY

[0196] As mentioned above, in the present invention, an active RC signalprocessing circuit comprises a feedforward section, and a feedbacksection. The feedforward section includes a CCVS providing a given gain,and the feedback section is operable to negatively feed back the outputof the feedforward section over the entire frequency range and provide agiven transfer characteristic. Thus, the present invention can providean active RC filter having a desired sensitivity of Q to variations ofassociated elements and a stable high-performance in high frequencybands without difficulties.

[0197] Through the negative feedback maintained over the entirefrequency range, s high Q-value can be stably obtained to facilitatenoise reduction in the active RC filter.

[0198] Further, the transfer characteristic of a signal processingcircuit can be determined substantially by the values of capacitors andresistors. Thus, signal processing circuits can be readily designedwithout using any inductance, and the miniaturization/integration insignal processing circuits can be facilitated.

What is claimed is:
 1. A low-noise active RC signal processing circuitcomprising: a feedforward section operable responsive to an input signalto provide an output at a predetermined gain; and a feedback sectionoperable responsive to the output of said forward circuit to negativelyfeed back said output to the input signal of said feedforward sectionwhile giving a predetermined transfer characteristic to said output, soas to allow said processing circuit to have a transfer impedancecharacteristic equal to or less than said predetermined gain over theentire frequency range.
 2. The low-noise active RC signal processingcircuit as defined in claim 1, wherein said feedforward section is acurrent-controlled voltage output circuit.
 3. The low-noise active RCsignal processing circuit as defined in claim 2, wherein saidcurrent-controlled voltage output circuit includes a common-basetransistor for receiving and inverting the input signal, and anemitter-follower transistor for outputting voltage, saidcurrent-controlled voltage output circuit having a transfer impedancedefining said predetermined gain.
 4. The low-noise active RC signalprocessing circuit as defined in claim 2, wherein saidcurrent-controlled voltage output circuit includes an operationalamplifier operable to invert the input signal, said operationalamplifier being subjected to feedback according to the transferimpedance defining said predetermined gain.
 5. The low-noise active RCsignal processing circuit as defined in either one of claims 1 to 3,wherein said feedback section is an active RC circuit having amultistage arrangement, said active RC circuit being operable to providea frequency-dependent characteristic to the output from said feedforwardsection.
 6. The low-noise active RC signal processing circuit as definedin either one of claims 1, 2 and 4, wherein said feedback section is avoltage-follower circuit operable to provide a frequency-dependentcharacteristic to the output from said feedforward section, saidvoltage-follower circuit including an operational amplifier and amultistage RC circuit.
 7. The low-noise active RC signal processingcircuit as defined in either one of claims 1 to 6, which is a bandpassfilter, wherein said transfer impedance characteristic defines thefrequency characteristic of said bandpass filter.
 8. The low-noiseactive RC signal processing circuit as defined in either one of claims 1to 6, which is a lowpass filter, wherein said transfer impedancecharacteristic defines the frequency characteristic of said lowpassfilter.
 9. The low-noise active RC signal processing circuit as definedin either one of claims 1 to 6, which is a highpass filter, wherein saidtransfer impedance characteristic defines the frequency characteristicof said highpass filter.